Our paper differs from these last two contributions In contrast to Olivier 2000

Our paper differs from these last two contributions

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Our paper differs from these last two contributions. In contrast to Olivier (2000), growth is enhanced by the existence of a bubble even if the bubble is on an unproductive asset. Therefore, the mechanism that allows to have a pro- ductive bubble in our framework is different. We also depart from Hirano and Yanagawa (2017) since we do not consider heterogenous investment projects and do not discuss the results according to the level of financial frictions. By inspection of Corollary 1 and Proposition 3, it is interesting to note that we can have ψ p lower than b ψ . 9 This means that for ψ p < ψ < b ψ , we can have a higher growth of the capital-labor ratio at the asymptotic bubbly BGP than at the bubbleless one ( γ * > γ wb ) even if young households are not short-sellers of the speculative asset. This is in contrast with Raurich and Seegmuller (2015, 2017) who study the existence of rational bubbles in overlapping generations economies with three period-lived households, vintage capital and exogenous growth. In both papers, capital is higher at the bubbly than at the bubbleless steady state only if either young or adult households are short-sellers of the bubble. Here, we obtain a different result, which means that the mechanism for the existence of a productive bubble is different than in these two papers. Our model with endogenous fertility and rational bubble also allows us to refer to the debate on the link between population size and the value of asset (Abel (2001), Geanakoplos et al. (2004), Poterba (2005)), which explains that asset price is higher when the relative number of savers is more significant. In particular, Geanakoplos et al. (2004) consider an overlapping generations model with three-period lived agents and identify that the number of savers is relatively more important as the ratio of middle-age over young households is higher. We contribute to this debate focusing on the price of the speculative asset. Obviously, the price of this asset is larger with the bubble than without. In the next corollary, we consider the range of parameter values for which the bubble is productive and we first make sure that, at the asymptotic bubbly BGP, middle-age households hold a larger amount of the bubble than young ones. Then, observing that the ratio of middle-age over young households is given by MY t N t - 1 / N t = 1/ n t , we denote by MY * and MY wb the value of this ratio evaluated at the asymptotic bubbly and bubbleless BGPs, respectively, and we compare them: Corollary 2. If A > A 1 , μ < μ nwb , ψ p < ψ < min { ψ b ; 1 } and α 6 β 1 + 2 β + β 2 , we have e b * 2 > n * e b * 1 , γ * > γ wb and n * < n wb , which means that MY * > MY wb . 9 We note that when Proposition 3 applies, it corresponds to case 2 of Corollary 1, because β 1 + 2 β + β 2 < β + β 2 1 + 2 β + 2 β 2 . Then, using (41) and (42), ψ p < b ψ requires μ < 1 - α ( 1 - α )+ α 2 ( β + β 2 ) α ( 1 - α ) .
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  • Spring '10
  • Economics, Capital accumulation

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